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DESCRIPTION: We say that a graph G is q-Ramsey for another graph H if any
q-coloring of the edges of G yields a monochromatic copy of H. Much of the
research related to Ramsey graphs is concerned with determining the smalle
st possible number of vertices in a q-Ramsey graph for a given H\, known as
the q-color Ramsey number of H . In the 1970s\, Burr\, Erdős\, and Lovász
initiated the study of another graph parameter in the context of Ramsey gr
aphs: the minimum degree. A straightforward argument shows that\, if G is
a minimal q-Ramsey graph for H\, then we must have δ(G) >\;= q(δ(H) - 1)
+ 1\, and we say that H is q-Ramsey simple if this bound can be attained. I
n this talk\, we will ask how typical Ramsey simplicity is\; more precisely
\, we will discuss for which pairs p and q the random graph G(n\,p) is almo
st surely q-Ramsey simple. This is joint work with Dennis Clemens\, Shagni
k Das\, and Pranshu Gupta.
DTSTAMP:20211020T164100
DTSTART:20211025T160000
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Informatik \n Takustr. 9
\n 14195 Berlin \n Room 005 (Ground Floor)
SEQUENCE:0
SUMMARY:Simona Boyadzhiyska (Freie Universität Berlin): Ramsey simplicity o
f random graphs
UID:107919307@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20211025-C-Boyadzhiyska.html
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